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# Rolling Dice

APSTAT-UPFEEW

Suppose at a local casino, a player rolls $4$ six-sided die.

The player wins a dollar each time he gets a $1$ or $2$ on one of the dice, so each game the player could win anywhere from $\$0$to$\$4$.

The player plays the game $100$ times and is disappointed with the outcome. He wonders if the dice are fair. Out of the $100$ trials, the player ended up with the following distribution of winnings:

Winnings \$0 \$1 \$2 \$3 \$4 Frequency 21 42 30 7 0 Is there sufficient evidence the dice are unfair? A Yes, at the$1\%, 5\%$, and$10\%$alpha levels. B Yes, at the$5\%$and$10\%$alpha levels, but not at the$1\%$level. C Yes, at the$10\%$alpha level, but not the$1\%$or$5\%$levels. D No, not at any of the common alpha levels of$1\%, 5\%$, or$10\%\$.

E

No, in fact, there is strong evidence the game is fair.